Quartic generator: deterministic acceptance

Builder/output: quartic.py, grav_noether.py, series_eval.py, jetpoly.py; P13_quartic_verified.json.

${\ell }_2,{\ell }_3,{\ell }_4$ are built from $L_{\Gamma \Gamma }$ and exported (exports/ell{2,3,4}_generating_polynomial.srepr; ${\ell }_4$ sha256 33ac9e49 e123, unchanged from p10; 3360 monomials, a reproducibility count only). Acceptance consists only of exact symbolic identities:

Identification of the exported coefficients. The independent evaluator computes $L_{\Gamma \Gamma }(\eta +\epsilon h)$ from its definition with the series inverse (C1) and the series $\sqrt{-q}$ (C2), truncated at ${\epsilon }^4$ (exact for $k\le 4$). C4 proves that the exports equal $-2[{\epsilon }^k]L_{\Gamma \Gamma }$ as polynomials, so no sampling is involved. C3 gives $L_{\Gamma \Gamma }=\sqrt{-g}R+{\partial }_{\mu }{B}^{\mu }$, hence $\int {\ell }_k=[{\kappa }^{k-2}]S_{\mathrm{EH}}$ for compact support. C5 compares, with the same sign and normalisation, against XVI-N grav_density.ell3_and_curvature (XII-C ${\ell }_3=-2(r_3+b_1{r}_2+b_2{r}_1)$), evaluated on symbolic second jets; the opposite sign is not a divergence. This is not a claim that XII-C is the quartic, and not a Ward identity. C7 is exact because $W_n$ is linear in $c$: $W_n\simeq c^{\mu }{E}_{c^{\mu }}(W_n)$, so $W_n$ is a divergence iff $E_{c^{\mu }}(W_n)\equiv 0$. At ${\kappa }^1$ and ${\kappa }^2$ the $s_0$ piece alone leaves 159 and 2088 terms per component, so the cancellation is genuinely mixed. Mutations (each rejected by a deterministic test): M1 one ${\ell }_4$ coefficient $\times \frac{7}{5}$ and M2 sign of ${\ell }_4$ (C7 at ${\kappa }^2$); M3 swapped contraction (C4 for all $k$, C5, C6, C7 at all orders); M4 missing ${\epsilon }^2$ coefficient of $\sqrt{-q}$ (C4 for ${\ell }_4$; C7 at ${\kappa }^2$); M5 wrong inverse sign (C1); M6 stale ${\ell }_4$ hash; M7 the p10 orientation $+{\partial }_{\mu }{B}^{\mu }$ (C3 generic and conformal).